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Math  /  Data & Statistics

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An urn contains one white ball and four black balls. You select balls randomly from the urn, one by one with replacement. If you select the white ball, then the game is finished. The probability that you finish the game in the third selection is a. (53)15\binom{5}{3} \frac{1}{5} b. 1/51 / 5 c. 1 d. (45)2(15)\left(\frac{4}{5}\right)^{2}\left(\frac{1}{5}\right) e. none of them

Studdy Solution
لحساب الاحتمال الكلي لإنهاء اللعبة في المحاولة الثالثة، نضرب الاحتمالات:
(45)×(45)×(15)=(45)2(15) \left(\frac{4}{5}\right) \times \left(\frac{4}{5}\right) \times \left(\frac{1}{5}\right) = \left(\frac{4}{5}\right)^{2} \left(\frac{1}{5}\right)
الاحتمال الكلي هو:
(45)2(15) \boxed{\left(\frac{4}{5}\right)^{2} \left(\frac{1}{5}\right)}

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